The immune response to varicella-zoster virus (VZV) will be studied in patients with Hodgkin's disease and non-Hodgkin's lymphoma who have a high incidence of VZV infections. These patients will be studied prospectively, at regular intervals, with sensitive methods for measuring VZV-specific antibody and cell-mediated immunity (CMI) in an effort to document their immune status prior to, during and after episodes of herpes zoster. These measurements will be related to the clinical disease status, antitumor therapy, and severity of disease in the study population. In addition, this closely monitored patient population will receive zoster immune globulin (ZIG) at frequent intervals in a controlled clinical trial to determine if exogenous antibody to VZV, administered prophylactically, will decrease the frequency of zoster occurrence. Similarly, when zoster occurs, ZIG or placebo will be administered therapeutically in a controlled trial to determine if ZIG can alter the clinical course of herpes zoster.